Skip to main content

Full text of "Analytical Mechanics"

See other formats


150
ANALYTICAL MECHANICS
XTOi                            /*W2
xdm+ I   xdm+   __ _-r_____ _ Jo _
r^m^- / t/O
2m
Similarly        y =
2m
2m
Therefore the mass of each body may be considered as being concentrated at its center of mass.
ILLUSTRATIVE EXAMPLE.
Find the center of mass of the plate indicated by the shaded part of Fig. 83.
(a) Suppose the plate to be separated into two parts by the dotted line. Then the coordinates of the center of mass of the lower part are
-           U              3                  U    U-
xi = -    and   2/1 = - 2                       2
On the other hand the coordinates of the center of mass of the upper part are
b  a        -,-      26  a
xz = -r    and   2/2 = ^----
Therefore the coordinates of the center of mass of the entire plate have the following values:
6  ,       6  a                                            6 
Wl + ^2
0-6(6 2 + oh - a2 2 (a + 6)
 a)a
&2 + ab - a2 2(a + 6